Thick-brane solutions and topology change transition on black hole backgrounds

We consider static, axisymmetric, thick-brane solutions on higher-dimensional, spherically symmetric black hole backgrounds. It was found recently [V.G. Czinner and A. Flachi, Phys. Rev. D 80, 104017 (2009).], that in cases in which the thick brane has more than two spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski-type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a nonperturbative approach. In the present paper, we provide an exact, numerical solution of the problem both for black hole- and Minkowski-type topologies with an arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a five-dimensional brane embedded in a six-dimensional bulk.